Problem: Solve for $x$ : $x^2 - x - 42 = 0$
The coefficient on the $x$ term is $-1$ and the constant term is $-42$ , so we need to find two numbers that add up to $-1$ and multiply to $-42$ The two numbers $6$ and $-7$ satisfy both conditions: $ {6} + {-7} = {-1} $ $ {6} \times {-7} = {-42} $ $(x + {6}) (x {-7}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 6) (x -7) = 0$ $x + 6 = 0$ or $x - 7 = 0$ Thus, $x = -6$ and $x = 7$ are the solutions.